Answer:
A triangle is equilateral if all three angles are same. but here two angles are 64° but third angle is 52°. so, Yin is incorrect.
Step-by-step explanation:
x = 19,
Putting value of x to find m∠ABC and m∠ACB
m∠ABC = (4x – 12)°
m∠ABC = (4(19) – 12)°
m∠ABC = (76 – 12)°
m∠ABC = 64°
m∠ACB = (2(19) + 26)°
m∠ACB = (38 + 26)°
m∠ACB = 64°
now we know sum of angles of triangle is 180°. We can find the measure of third angle.
180 = 64+64 +x
x= 180 - 64 - 64
x = 52°
A triangle is equilateral if all three angles are same. but here two angles are 64° but third angle is 52°. so, Yin is incorrect.
Sample Response: No, Yin is not correct. If
x = 19, the measure of angle ABC = 4(19) – 12 = 64. Therefore, the two base angles measure 64°. An equilateral triangle is equiangular, so each angle would have to measure 60° because there are 180° in a triangle.
What did you include in your response? Check all that apply.
Yin is not correct.
The measure of the congruent base angles is 64°.
The measures of the angles in an equilateral triangle are 60°.
A new movie is released each year for 10 years to go along with a popular book series. Each movie is 4 minutes longer than the last to go along with a plot twist. The first movie is 60 minutes long. Use an arithmetic series formula to determine the total length of all 10 movies.
The sum of the length of all the ten movies is [tex]\fbox{\begin\\\ 780\text{ minutes}\\\end{minispace}}[/tex].
Step-by-step explanation:
It is given that a new movie is released each year for [tex]10[/tex] consecutive years so there are total number of [tex]10[/tex] movies released in [tex]10[/tex] years.
The movie released in first year is [tex]60\text{ minutes}[/tex] long and each movie released in the successive year is [tex]4\text{ minutes}[/tex] longer than the movie released in the last year.
So, as per the above statement movie released in first year is [tex]60[/tex] minutes long, movie released in second year is [tex]64[/tex] minutes long, movie released in third year is [tex]68[/tex] minutes long and so on.
The sequence of the length of the movie formed is as follows:
[tex]\fbox{\begin\\\ 60,64,68,72...\\\end{minispace}}[/tex]
The sequence formed above is an arithmetic sequence.
An arithmetic sequence is a sequence in which the difference between the each successive term and the previous term is always constant or fixed throughout the sequence.
The general term of an arithmetic sequence is given as
[tex]\fbox{\begin\\\math{a_{n} =a+(n-1)d}\\\end{minispace}}[/tex]
The sequence formed for the length of the movie is an arithmetic sequence in which the first term is [tex]60[/tex] and the common difference is [tex]4[/tex].
The arithmetic series corresponding to the arithmetic sequence of length of the movie is as follows:
[tex]\fbox{\begin\\\ 60+64+68+72+...\\\end{minispace}}[/tex]
The arithmetic series formula to obtain the sum of the above series is as follows:
[tex]\fbox{\begin\\\math{S_{n} =(n/2)(2a+(n-1)d)}\\\end{minispace}}[/tex]
In the above equation [tex]n[/tex] denotes the total number of terms, a denotes the first term, d denotes the common difference and Sn denotes the sum of n terms of the series.
Substitute [tex]\fbox{\begin\\\math{a}=60\\\end{minispace}}[/tex],[tex]\fbox{\begin\\\math{n}=10\\\end{minispace}}[/tex] and [tex]\fbox{\begin\\\math{d}=4\\\end{minispace}}[/tex] in the equation [tex]\fbox{\begin\\\math{S_{n} =(n/2)(2a+(n-1)d)}\\\end{minispace}}[/tex]
[tex]S_{10} =(10/2)(120+36) \\S_{10} =780[/tex]
Therefore, the length of the all [tex]10[/tex] movies as calculated above is [tex]\fbox{\begin\\\ 780\text{ minutes}\\\end{minispace}}[/tex]
Learn more:
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Grade: Middle school
Subject: Mathematics
Chapter: Arithemetic preogression
Keywords: Sequence, series, arithmetic , arithmetic sequence, arithmetic series, common difference, sum of series, pattern, arithmetic pattern, progression, arithmetic progression, successive terms.
Answer:
The total length of all 10 movies is 780 minutes.
Further Explanation:
Arithmetic Sequence: A sequence of numbers in which difference of two successive numbers is constant.
The sum of n terms of an arithmetic sequence is given by the formula,
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
Where,
a is the first term of the sequence. d is a common difference.n is number of terms[tex]S_n[/tex] is sum of n terms of the sequence.The first movie is 60 minutes long. This would be the first term of the sequence.
Thus, First term, a= 60 minutes
A new movie is released each year for 10 years. In 10 years total 10 movies will released.
Thus, Number of terms, n=10
Each movie is 4 minutes longer than the last released movie. It means the difference of length of two successive movie is 4 minutes.
Thus, Common difference, d=4
Using the sum of arithmetic sequence formula, the total length of all 10 movies is,
[tex]S_{10}=\dfrac{10}{2}[2\cdot 60+(10-1)\cdot 4][/tex]
[tex]S_{10}=\dfrac{10}{2}[2\cdot 60+9\cdot 4][/tex] [tex][\because 10-1=9][/tex]
[tex]S_{10}=\dfrac{10}{2}[120+36][/tex] [tex][\because 2\cdot 60=120\text{ and }9\cdot 4=36][/tex]
[tex]S_{10}=\dfrac{10}{2}\times 156[/tex] [tex][\because 120+36=156][/tex]
[tex]S_{10}=5\times 156[/tex] [tex][\because 10\div 2=5][/tex]
[tex]S_{10}=780[/tex] [tex][\because 5\times 156=780][/tex]
Therefore, The total length of all 10 movies is 780 minutes
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Find sum: https://brainly.com/question/11741302
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Keywords:
Arithmetic sequence, Arithmetic Series, Common difference, First term, AP progression, successive number, sum of natural number.
Solve the triangle. a = 12, b = 22, C = 95°
Answer:
a = 12
b = 22
c = 25.96186
Angle A = 27.417°
Angle B = 57.583°
Angle C = 95°
Area = 131.4977
Perimeter = 59.96186
a = 12,b = 22,c = 25.96186
∠A = 27.417°,∠B = 57.583°,∠C = 95°
What is law of sine?Law of sine states that the ratio sine of an angle and its opposite side in a triangle is same for all 3 angles and their corresponding sides.
sinA/a=sinB/b=sinC/c
What is law of cosine?Law of cosine is the generalized Pythagoras theorem is applied. It is applied for measuring one side where the opposite angle and other two sides are given.
c²=a²+b²-2abcosC
here given,
a = 12
b = 22
∠C = 95°
Applying law of cosine,
c²=a²+b²-2abcosC
=12²+22²-2.12.22.cos95°
=674.018
⇒c=√674.018
⇒c=25.96
Applying law of sine
sinA/a=sinC/c
⇒sinA=(a/c)sinC
⇒sinA=(12/25.96)sin95°=0.46
⇒A=sin⁻¹(0.46)
⇒A=27.417°
As we know sum of the 3 angles in a triangles are 180°.
∠B=180°-(∠A+∠C)=180°-(27.417°+95°)=180°-(122.42)
⇒∠B=57.583°
Therefore a = 12,b = 22,c = 25.96186
∠A = 27.417°,∠B = 57.583°,∠C = 95°
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Can someone helpppppp
Answer:
13.7
Step-by-step explanation:
We know that sin(thetha) = BC/AB
In this case, thetha = 41, BC = 9in
→ AB = BC/sin(thetha)
→ AB = 9in/sin(41)
→ AB = 13.7
Therefore, the result is 13.7
Answer:
The correct answer is third option
13.8 in
Step-by-step explanation:
From the figure we can see a right angled triangle ABC, right angled at C,
m<A = 41°, and BC = 9 in
Points to remember
Sin θ = Opposite side/Hypotenuse
To find the value of AB
Sin 41 = Opposite side/Hypotenuse
= BC/AB
= 9/AB
AB = 9/Sin(41)
=13.8 in
The correct answer is third option
13.8 in
Prove that the segments joining the midpoint of consecutive sides of an isosceles trapezoid form a rhombus.
Find the slope of DE and FG.
Answer:
See explanation
Step-by-step explanation:
a) To prove that DEFG is a rhombus, it is sufficient to prove that:
All the sides of the rhombus are congruent: [tex]|DG|\cong |GF| \cong |EF| \cong |DE|[/tex]The diagonals are perpendicularUsing the distance formula; [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]|DG|=\sqrt{(0-(-a-b))^2+(0-c)^2}[/tex]
[tex]\implies |DG|=\sqrt{a^2+b^2+c^2+2ab}[/tex]
[tex]|GF|=\sqrt{((a+b)-0)^2+(c-0)^2}[/tex]
[tex]\implies |GF|=\sqrt{a^2+b^2+c^2+2ab}[/tex]
[tex]|EF|=\sqrt{((a+b)-0)^2+(c-2c)^2}[/tex]
[tex]\implies |EF|=\sqrt{a^2+b^2+c^2+2ab}[/tex]
[tex]|DE|=\sqrt{(0-(-a-b))^2+(2c-c)^2}[/tex]
[tex]\implies |DE|=\sqrt{a^2+b^2+c^2+2ab}[/tex]
Using the slope formula; [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The slope of EG is [tex]m_{EG}=\frac{2c-0}{0-0}[/tex]
[tex]\implies m_{EG}=\frac{2c}{0}[/tex]
The slope of EG is undefined hence it is a vertical line.
The slope of DF is [tex]m_{DF}=\frac{c-c}{a+b-(-a-b)}[/tex]
[tex]\implies m_{DF}=\frac{0}{2a+2b)}=0[/tex]
The slope of DF is zero, hence it is a horizontal line.
A horizontal line meets a vertical line at 90 degrees.
Conclusion:
Since [tex]|DG|\cong |GF| \cong |EF| \cong |DE|[/tex] and [tex]DF \perp FG[/tex] , DEFG is a rhombus
b) Using the slope formula:
The slope of DE is [tex]m_{DE}=\frac{2c-c}{0-(-a-b)}[/tex]
[tex]m_{DE}=\frac{c}{a+b)}[/tex]
The slope of FG is [tex]m_{FG}=\frac{c-0}{a+b-0}[/tex]
[tex]\implies m_{FG}=\frac{c}{a+b}[/tex]
(Help!!will give Brainest, if correct)
A system of inequalities can be used to determine the depth of a toy, in meters, in a pool depending on the time, in seconds, since it was dropped. Which constraint could
be part of the scenario?
A)The pool is 1 meter deep.
B)The pool is 2 meters deep.
C)The toy falls at a rate of at least a 1/2
meter per second.
D)The toy sinks at a rate of no more than a
1/2 meter per second
In the given scenario regarding a toy sinking in a pool, the constraints related to the depth of the pool and the rate of sinking of the toy could be part of the scenario, which illustrates a system of inequality related to the depth of the toy in the pool over time.
Explanation:The question requires understanding of the constraints in a scenario that involve a system of inequalities related to the depth of a toy in a pool over time. In this case, the toy is falling, or sinking, into the pool. Therefore, the scenario will involve the depth of the pool and the rate at which the toy is falling.
Firstly, The depth of the pool is important because the toy cannot sink deeper than the pool is. Therefore, both constraints A) The pool is 1 meter deep and B) The pool is 2 meters deep could both be part of the scenario, depending on the actual depth of the pool involved.
Secondly, The rate at which the toy is falling (sinking) is also important. Both constraints C) The toy falls at a rate of at least a 1/2 meter per second and D) The toy sinks at a rate of no more than a 1/2 meter per second could be part of the scenario, depending on the actual sinking rate of the toy.
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The constraint that could be part of the scenario is that the D) toy sinks at a rate of no more than a 1/2 meter per second.
Explanation:A system of inequalities is a set of two or more inequalities involving the same variables. The solution to the system is the set of values that satisfy all the inequalities simultaneously. Graphically, the solution represents the overlapping region of the individual inequalities on a coordinate plane.
The constraint that could be part of the scenario is that the toy sinks at a rate of no more than a 1/2 meter per second. This constraint ensures that the depth of the toy in the pool does not change too rapidly. If the toy sank at a faster rate than 1/2 meter per second, it would quickly reach the bottom of the pool.
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What is the y-intercept of the line given by the equation y=5x-21
O A. (0.21)
O B. (0,5)
O C. (0, -21)
O D. (0,-5)
Answer: C.( 0,-21)
Step-by-step explanation: Use the slope-intercept form to find the slope and y-intercept.
Final answer:
The y-intercept of the given line y = 5x - 21 is -21, which means the line crosses the y-axis at the point (0, -21), corresponding to option C.
Explanation:
The y-intercept of a line represented by the equation y = mx + b is the value at which the line crosses the y-axis. To find the y-intercept, one must look at the value of b, which is the constant in the equation. Given the equation y = 5x - 21, the y-intercept would be -21.
Therefore, when x is 0, the value of y would be -21, meaning that the line crosses the y-axis at the point (0, -21). This corresponds to the option C: (0, -21).
The points (3, 24) and (7, 56) represent points of a function where y, the number of photographs, varies directly with x, the number of pages in an album. Which statement describes another point on the graph of this function?
A 50-page photo album holds 400 photographs.
An 80-page photo album holds 560 photographs.
A 100-page photo album holds 8,000 photographs.
A 900-page photo album holds 8,400 photographs.
Answer:
Option A 50-page photo album holds 400 photographs.
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
step 1
Find the value of k
For the point (3,24)
x=3,y=24
k=y/x
k=24/3=8
The equation is equal to
y=8x
step 2
Verify each statement
case A) 50-page photo album holds 400 photographs.
For x=50
substitute in the equation
y=8(50)=400 -----> is correct
case B) 80-page photo album holds 560 photographs.
For x=80
substitute in the equation
y=8(80)=640 -----> is not correct
case C) 100-page photo album holds 8,000 photographs.
For x=100
substitute in the equation
y=8(100)=800 -----> is not correct
case D) 900-page photo album holds 8,400 photographs.
For x=900
substitute in the equation
y=8(900)=7,200 -----> is not correct
Answer:
Yes ! The correct answer is A.) 50-page photo album holds 400 photographs.
Step-by-step explanation:
I did the Unit Test and i got it correct.
What is the median of the distribution?
Answer:
5.
Step-by-step explanation:
There are a total of 21 items so the median is the mean of the 10th and 11th .
This lies on the highest column so the median is 5.
Write an equation for a circle with a diameter that has endpoints at (–4, –7) and (–2, –5). Round to the nearest tenth if necessary. Question 9 options: (x + 3)2 + (y + 6)2 = 2 (x + 3)2 + (y + 6)2 = 8 (x – 3)2 + (y – 6)2 = 2 (x – 3)2 + (y – 6)2 = 8
since we know the endpoints of the circle, we know then that distance from one to another is really the diameter, and half of that is its radius.
we can also find the midpoint of those two endpoints and we'll be landing right on the center of the circle.
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{diameter}{d}=\sqrt{[-2-(-4)]^2+[-5-(-7)]^2}\implies d=\sqrt{(-2+4)^2+(-5+7)^2} \\\\\\ d=\sqrt{2^2+2^2}\implies d=\sqrt{2\cdot 2^2}\implies d=2\sqrt{2}~\hfill \stackrel{~\hfill radius}{\cfrac{2\sqrt{2}}{2}\implies\boxed{ \sqrt{2}}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-5})\qquad \qquad \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{-2-4}{2}~~,~~\cfrac{-5-7}{2} \right)\implies \left( \cfrac{-6}{2}~,~\cfrac{-12}{2} \right)\implies \stackrel{center}{\boxed{(-3,-6)}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-3}{ h},\stackrel{-6}{ k})\qquad \qquad radius=\stackrel{\sqrt{2}}{ r} \\[2em] [x-(-3)]^2+[y-(-6)]^2=(\sqrt{2})^2\implies (x+3)^2+(y+6)^2=2[/tex]
Answer:
FIRST OPTION: [tex](x+3)^2+ (y+6)^2 =2[/tex]
Step-by-step explanation:
The equation of the circle in center-radius form is:
[tex](x- h)^2 + (y- k)^2 = r^2[/tex]
Where the center is at the point (h, k) and the radius is "r".
We know that the endpoints of the diameter of this circle are (-4, -7) and (-2, -5), so we can find the radius and the center of the circle.
In order to find the radius, we need to find the diameter. To do this, we need to use the formula for calculate the distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Then, substituting the coordinates of the endpoints of the diameter into this formula, we get:
[tex]d=\sqrt{(-4-(-2))^2+(-7-(-5))^2}=2\sqrt{2}[/tex]
Since the radius is half the diameter, this is:
[tex]r=\frac{2\sqrt{2}}{2}=\sqrt{2}[/tex]
To find the center, given the endpoints of the diameter, we need to find the midpoint with this formula:
[tex]M=(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})[/tex]
This is:
[tex]M=(\frac{-4-2}{2},\frac{-7-5}{2})=(-3,-6)[/tex]
Then:
[tex]h=-3\\k=-6[/tex]
Finally, substituting values into [tex](x- h)^2 + (y- k)^2 = r^2[/tex], we get the following equation:
[tex](x- (-3))^2 + (y- (-6))^2 = (\sqrt{2})^2[/tex]
[tex](x+3)^2+ (y+6)^2 =2[/tex]
What is the slope of a line that is perpendicular to the line x = –3? –3 0 1/3 undefined
I know the answer is 0, but I would love it if someone could give an explanation of why...thanks!
Answer:
slope = 0
Step-by-step explanation:
The line with equation x = - 3 is a vertical line parallel to the y- axis
A perpendicular line is therefore a horizontal line parallel to the x- axis
The slope of the x- axis is zero, hence the slope of the horizontal line is
slope = 0
8. A basketball with a diameter of 9.5 inches
is packaged in a cubic box measuring
9.5 inches on each edge. Determine the
volume of the empty space in the box.
The correct answer is [tex]\(\boxed{\frac{1919}{16} - \frac{481\pi}{128}}\)[/tex] cubic inches.
To determine the volume of the empty space in the box, we need to calculate the volume of the box and the volume of the basketball, and then subtract the volume of the basketball from the volume of the box.
First, let's calculate the volume of the cubic box. Since the edge of the cube is given as 9.5 inches, the volume of the cube [tex]\( V_{box} \)[/tex] is the edge length cubed:
[tex]\[ V_{box} = 9.5^3 \][/tex]
[tex]\[ V_{box} = \left(\frac{95}{10}\right)^3 \][/tex]
[tex]\[ V_{box} = \frac{95^3}{10^3} \][/tex]
[tex]\[ V_{box} = \frac{95^3}{1000} \][/tex]
[tex]\[ V_{box} = \frac{857375}{1000} \][/tex]
[tex]\[ V_{box} = \frac{1919}{4} \][/tex] cubic inches.
Next, we calculate the volume of the basketball. The basketball is a sphere with a diameter of 9.5 inches, so its radius [tex]\( r \)[/tex] is half of that:
[tex]\[ r = \frac{9.5}{2} \][/tex]
[tex]\[ r = \frac{95}{20} \][/tex]
[tex]\[ r = \frac{19}{4} \] inches.[/tex]
The volume of a sphere [tex]\( V_{sphere} \)[/tex] is given by the formula:
[tex]\[ V_{sphere} = \frac{4}{3}\pi r^3 \][/tex]
[tex]\[ V_{sphere} = \frac{4}{3}\pi \left(\frac{19}{4}\right)^3 \][/tex]
[tex]\[ V_{sphere} = \frac{4}{3}\pi \left(\frac{19^3}{4^3}\right) \][/tex]
[tex]\[ V_{sphere} = \frac{4}{3}\pi \left(\frac{6859}{64}\right) \][/tex]
[tex]\[ V_{sphere} = \frac{481\pi}{128} \] cubic inches.[/tex]
Now, we subtract the volume of the basketball from the volume of the box to find the volume of the empty space [tex]\( V_{empty} \):[/tex]
[tex]\[ V_{empty} = V_{box} - V_{sphere} \][/tex]
[tex]\[ V_{empty} = \frac{1919}{4} - \frac{481\pi}{128} \] cubic inches.[/tex]
To simplify the expression, we can multiply the terms by a common denominator of 128 to combine them:
[tex]\[ V_{empty} = \frac{1919 \times 32}{128} - \frac{481\pi}{128} \][/tex]
[tex]\[ V_{empty} = \frac{61408}{128} - \frac{481\pi}{128} \][/tex]
[tex]\[ V_{empty} = \frac{61408 - 481\pi}{128} \] cubic inches.[/tex]
However, we notice that the denominator of 128 can be simplified by dividing both numerator and denominator by 4, which gives us the final
[tex]\[ V_{empty} = \frac{1919}{16} - \frac{481\pi}{128} \][/tex] cubic inches.
Therefore, the volume of the empty space in the box is [tex]\(\boxed{\frac{1919}{16} - \frac{481\pi}{128}}\)[/tex] cubic inches.
a man bought two calculators at rupees 1250.he sold one at a profit of 2%and next at loss of 3% find cp
Answer:
the required answer is 125/24.
Answer:
The cost price of one calculator is Rs.750.
The cost price of other calculator is Rs.500.
Step-by-step explanation:
Cost price of 1'st calculator = x
Cost price of 2'nd calculator = 1250-x
He sold one at a profit of 2%.
The selling price of one calculator is
[tex]SP_1=CP(1+\frac{P\%}{100})[/tex]
[tex]SP_1=x(1+\frac{2}{100})[/tex]
[tex]SP_1=x(1+0.02)[/tex]
[tex]SP_1=1.02x[/tex]
He sold other at a loss of 3%.
The selling price of other calculator is
[tex]SP_2=CP(1-\frac{L\%}{100})[/tex]
[tex]SP_2=(1250-x)(1-\frac{3}{100})[/tex]
[tex]SP_2=(1250-x)(1-0.03)[/tex]
[tex]SP_2=(1250-x)(0.97)[/tex]
[tex]SP_2=1212.5-0.97x[/tex]
According to given condition,
[tex]SP_1+SP_2=1250[/tex]
[tex]1.02x+1212.5-0.97x=1250[/tex]
[tex]0.05x=1250-1212.5[/tex]
[tex]0.05x=37.5[/tex]
[tex]x=\frac{37.5}{0.05}[/tex]
[tex]x=750[/tex]
The cost price of one calculator is Rs.750.
The cost price of other calculator is 1250-750=Rs.500.
Which Congruence Statement Is Correct For These Triangles?
Answer:
D. ABC = DBC
Step-by-step explanation:
They are the same length and congruent.
Answer:
d) ABC ≅ DBC
Step-by-step explanation:
∠B in ΔABC and ∠B in ΔDBC is 90°. BC is a common side in both triangles which mean that both triangles have one side of the same length. Side AC in ΔABC is the same length as side DC in ΔDBC. Therefore ∠C in both ΔABC and ΔDBC are the same size. Therefore ΔDBC is a mirror image of ΔABC, which is a form of congruent triangles.
Write the function , √(x^3+6)/√(x^3-9) as a composition of three or more non-identity functions.
Answer:
[tex]h \circ m \circ n \text{ where } h(x)=\sqrt{x} \text{ and } m(x)=1+\frac{15}{n} \text{ and } n(x)=x^3-9[/tex]
Step-by-step explanation:
Ok so I see a square root is on the whole thing.
I'm going to let the very outside function by [tex]h(x)=sqrt(x)[/tex].
Now I'm can't just let the inside function by one function [tex]g(x)=\frac{x^3+6}{x^3-9}[/tex] because we need three functions.
So I'm going to play with [tex]g(x)=\frac{x^3+6}{x^3-9}[/tex] a little to simplify it.
You could do long division. I'm just going to rewrite the top as
[tex]x^3+6=x^3-9+15[/tex].
[tex]g(x)=\frac{x^3-9+15}{x^3-9}=1+\frac{15}{x^3-9}[/tex].
So I'm going to let the next inside function after h be [tex]m(x)=1 + \frac{15}{x}[/tex].
Now my last function will be [tex]n(x)=x^3-9[/tex].
So my order is h(m(n(x))).
Let's check it:
[tex]h(m(x^3-9))[/tex]
[tex]h(1+\frac{15}{x^3-9})[/tex]
[tex]h(\frac{x^3-9+15}{x^3-9})[/tex]
[tex]h(\frac{x^3+6}{x^3-9})[/tex]
[tex]\sqrt{ \frac{x^3+6}{x^3-9}}[/tex]
To express the function √(x^3+6)/√(x^3-9) as a composition of non-identity functions, we can rewrite it in terms of exponential and logarithmic functions.
Explanation:To express the function √(x^3+6)/√(x^3-9) as a composition of three or more non-identity functions, we can start by rewriting √(x^3+6) and √(x^3-9) as powers:
√(x^3+6) = (x^3+6)^(1/2)
√(x^3-9) = (x^3-9)^(1/2)
Next, we can express (x^3+6)^(1/2) and (x^3-9)^(1/2) in terms of powers of its components. Let's denote a = x^3+6 and b = x^3-9:
(x^3+6)^(1/2) = (a)^(1/2)
(x^3-9)^(1/2) = (b)^(1/2)
Finally, we can express these in terms of exponential and logarithmic functions:
(a)^(1/2) = e^(0.5ln(a))
(b)^(1/2) = e^(0.5ln(b))
Therefore, the function √(x^3+6)/√(x^3-9) can be expressed as a composition of three non-identity functions:
√(x^3+6)/√(x^3-9) = e^(0.5ln(a))/e^(0.5ln(b))
The spinner of the compass is two congruent isosceles triangles connected by their bases as shown in the diagram. The base of each of these triangles is 2 centimeters and the legs are 5 centimeters.
If the metal used to construct the spinner costs $13.25 per square centimeter, how much will it cost to make this part of the compass? Round to the nearest cent.
Cost =
Answer:
fff
Step-by-step explanation:
By pythagorean theorum we calculate the height:
[tex]\sqrt{5^2-1^2}[/tex]
=[tex]\sqrt{24}[/tex] = height of triangle
area of triangle = base * height
area = [tex]2*\sqrt{24}[/tex]
There are two triangles so:
[tex]2*2*\sqrt{24}=4\sqrt{24}[/tex]
Multiply this by 13.25 to get total cost:
=$259.65
Answer:
$ 129.82 because it is to the nearest cent
How much money should be invested today in an account that earns 3.5%, compound daily, in order to accumulate $75000 in 10 years (assume n=365)
[tex]\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill &\$75000\\ P=\textit{original amount deposited}\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ t=years\dotfill &10 \end{cases} \\\\\\ 75000=Pe^{0.035\cdot 10}\implies 75000=Pe^{0.35}\implies \cfrac{75000}{e^{0.35}}=P \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 52851.61\approx P~\hfill[/tex]
Solve for x,y, and z
Answer:
Part A) [tex]x=6[/tex]
Part B) ∠3=29°
Part C) ∠1=29°
Part D) ∠2=151°
Step-by-step explanation:
Part A) If ∠3=5x-1 and ∠5=3x+11, then x=?
we know that
∠3=∠5 ----> by alternate interior angles
so
substitute and solve for x
[tex]5x-1=3x+11[/tex]
[tex]5x-3x=11+1[/tex]
[tex]2x=12[/tex]
[tex]x=6[/tex]
Part B) If ∠3=5x-1 and ∠5=3x+11, then the measure of ∠3=?
we know that
∠3=5x-1
The value of x is
[tex]x=6[/tex]
substitute
∠3=5(6)-1=29°
Part C) If ∠3=5x-1 and ∠5=3x+11, then the measure of ∠1=?
we know that
∠1=∠3 ----> by vertical angles
we have
∠3=29°
therefore
∠1=29°
Part D) If ∠3=5x-1 and ∠5=3x+11, then the measure of ∠2=?
we know that
∠1+∠2=180° ----> by supplementary angles
we have
∠1=29°
substitute
29°+∠2=180°
∠2=180°-29°
∠2=151°
Determine two pairs of polar coordinates for the point (3, -3) with 0°≤ θ < 360°
Answer:
[tex]\left ( 3\sqrt{2},135^{\circ} \right )\,,\,\left ( 3\sqrt{2},315^{\circ} \right )[/tex]
Step-by-step explanation:
Let (x,y) be the rectangular coordinates of the point.
Here, [tex](x,y)=(3,-3)[/tex]
Let polar coordinates be [tex](r,\theta )[/tex] such that [tex]r=\sqrt{x^2+y^2}\,,\,\theta =\arctan \left ( \frac{y}{x} \right )[/tex]
[tex]r=\sqrt{3^2+(-3)^2}=\sqrt{18}=3\sqrt{2}[/tex]
[tex]\theta =\arctan \left ( \frac{-3}{3} \right )= \arctan (-1)[/tex]
We know that tan is negative in first and fourth quadrant, we get
[tex]\theta =\pi-\frac{\pi}{4}=\frac{3\pi}{4}=135^{\circ}\\\theta =2\pi-\frac{\pi}{4}=\frac{7\pi}{4}=315^{\circ}[/tex]
So, polar coordinates are [tex]\left ( 3\sqrt{2},135^{\circ} \right )\,,\,\left ( 3\sqrt{2},315^{\circ} \right )[/tex]
What is the circumference of a circle, radius 8cm
Answer: C≈50.27cm
if u want the solution then here u go
C=2πr=2·π·8≈50.26548cm
if g(x) = x^2+3 find g(4)
A .11
B. 19
C. 16
D. 8
Answer:
B. 19
Step-by-step explanation:
g(x) = x^2+3
Let x=4
g(4) = 4^2 +3
= 16+3
=19
Answer:
b
Step-by-step explanation:
all work is shown and pictured
Which statement is true of the function f(x) = -3/x? Select three options.
The function is always increasing.
The function has a domain of all real numbers.
The function has a range of {yl-
The function is a reflection of y = 3.
The function passes through the point (3,-27).
We have the following function:
[tex]f(x)=-\frac{3}{x}[/tex]
The graph of this function has been plotted below. So lets analyze each statement:
1. The function is always increasing. FalseAs you can see x increases from -∞ to 0 and decreases from 0 to +∞
2. The function has a domain of all real numbers. FalseThe function is undefined for [tex]x=0[/tex] since x is in the denominator.
3. The function has a range of {yl-Statement is unclear but the range is the set of all real numbers except zero.
4. The function is a reflection of y = 3. FalseThe function is a reflection in the x axis of the function [tex]g(x)=\frac{3}{x}[/tex]
5. The function passes through the point (3,-27).FalseThis is false since:
[tex]f(3)=-1\neq -27[/tex]
Note. As you can see those statements are false, so any of them is true, except item 3 that is unclear.
Answer:
its b and d
Step-by-step explanation:
i know
Cary earns $975 each month on his part-time job. How much money does he earn in a year
Answer:
$11,700
Step-by-step explanation:
If Cary earns $975 each month on his part-time job, he would earn $11,700 in a year.
1 year = 12 months
$975 per month
975 x 12 = 11700
In this question, we're going to need to find out how much Cary earns in a year.
To do this, we need to go back to the problem to see if we can get some valuable information.
We know that Cary earns $975 each month.
With the information above, we can solve the problem.
There are 12 months in a year, so that means we're going to multiply 975 by 12 in order to find out how much Cary earns in a year.
975 × 12 = 11,700
When you multiply, you would end up with the answer "11,700"
This means that Cary earns $11,700 in a year
I hope this helps you outGood luck with your academics-JimHow would I do this problem?
Answer:
Step-by-step explanation:
The sum of the interior angles of an n gon is found by using the following formula.
(n-2)*180 = sum of the interior angles.
(n - 2) * 180 = 3960 Divide by 180
(n - 2) 180/180 = 3960/180 Show the division
n - 2 = 22 Add 2 to both sides.
n -2+2=22+2 Combine
n = 24
======================================
To find the size of each angle, use
(n - 2)*180/n
(24 - 2)*180/24
22 * 180/24
3960/24 = 165
===========
another way
===========
You already know there are 24 sides. You are given the sum of the interior angles as 3960
All you really need to do is 3960/24 = 165
Ms. Nichols rated her theater students' singing and dancing skills using a scale of 0 through 10. What relationship does the scatter plot BEST reveal about dancing skills and singing skills?
Answer:
There is no scatter plot provided, but I can tell you how to solve this. You will look at the plot. It should be numbered somewhere 0-10 and tell you that is the point system, the other side should be the students. So, now you will look at the points on the plot and determine where most of them are. If they are low, you would say that she thinks that they are bad. If it's mostly middle, you would say they need improvement, but aren't terrible. If they are high, you would say she thinks that they are very good.
Alex purchased a new suit
discounted by 65%.
He paid $35.80 for the suit.
What was its original price?
HELP
Answer:
$102.29 is the original price of the suit.
Explanation:
$x ------- 100% price (full price)
$35.80 --------------- 35% of the original price (100%-65%=35%).
To find x, use cross-products.
x=(35.80×100)/35 =3580/35 = approximately $102.29.
Answer:
The original price of the suit was $102.29.
Step-by-step explanation:
Alex purchased a new suit discounted by 65%.
He paid $35.80 for the suit.
Let the original price (100% price) be x.
After discount the price is given = 100% - 65% = 35%
35% of x = 35.80
0.35x = 35.80
x = [tex]\frac{35.80}{0.35}[/tex]
x = 102.2857 rounded to $102.29
The original price of the suit was $102.29.
help with inverse please
as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables, and then solve for "y".
[tex]\bf y = 4x^2-8\implies \stackrel{\textit{quick switcheroo}}{\underline{x} = 4\underline{y}^2-8}\implies x+8=4y^2\implies \cfrac{x+8}{4}=y^2 \\\\\\ \sqrt{\cfrac{x+8}{4}}=y\implies \cfrac{\sqrt{x+8}}{\sqrt{4}}=y\implies \cfrac{\sqrt{x+8}}{2}=\stackrel{f^{-1}(x)}{y}[/tex]
Graph the equation below
Answer:
See picture.
In the picture I graphed (0,1) and then graphed (1,3).
I connected the points with a straight-edge.
Step-by-step explanation:
This question is asking us to use slope-intercept form of a line to answer it.
Slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.
Your equation is y=2x+1 so our m=2 and b=1.
So our y-intercept is 1. This is the first point we graph.
The slope is 2 or as a fraction 2/1. Recall that slope=rise/run. So this tells us after we plot (0,1) we need to go up 2 units and right 1 unit to get one more point to graph. This point will be (0+1,1+2) or just (1,3).
I will draw a graph also to show you this:
Answer:
Graph Attached Below
Step-by-step explanation:
Hello!
To graph a line, we just need any two points that belong to that line.
We know the y-intercept, (0,1), given in the equation itself. We can plot that point as our first point.
The second point can be found by using the slope. The slope is 2/1, and we can go up 2 units and to the right 1 unit to find the second point.
The second point is (1,3).
Given point (-6, -3) and a slope of 4, write an equation in point-slope form. a. y - 3 = 4(x - 6) c. y + 3 = 4(x + 6) b. y + 3 = 4(x - 6) d. y - 3 = 4(x + 6) Please select the best answer from the choices provided A B C D
For this case we have that by definition, the point-slope equation of a line is given by:
[tex]y-y_ {0} = m (x-x_ {0})[/tex]
We have as data that:
[tex](x_ {0}, y_ {0}): (- 6, -3)\\m = 4[/tex]
Substituting in the equation we have:
[tex]y - (- 3) = 4 (x - (- 6))\\y + 3 = 4 (x + 6)[/tex]
Finally, the equation is: [tex]y + 3 = 4 (x + 6)[/tex]
Answer:
[tex]y + 3 = 4 (x + 6)[/tex]
[tex]\huge{\boxed{y+3=4(x+6)}}[/tex]
Point-slope form is [tex]y-y_1=m(x-x_1)[/tex], where [tex]m[/tex] is the slope and [tex](x_1, y_1)[/tex] is a known point on the line.
Substitute in the values. [tex]y-(-3)=4(x-(-6))[/tex]
Simplify the negative subtraction. [tex]\boxed{y+3=4(x+6)}[/tex]
which of the following is equivalent to
6(2y - 4) + p
A. p+ 12y - 24
B. 6y + p - 24
C. p - 6(2y - 4)
D. 24 + 12y + p
Plz explain or show work on how you got the answer :)
The expression equivalent to 6(2y - 4) + p is p + 12y - 24, according to the distributive property of multiplication over subtraction.
Explanation:The task is to find which of the following is equivalent to 6(2y - 4) + p. The first step is to apply the distributive property of multiplication over subtraction to the term 6(2y - 4). This gives us 12y - 24. If we add p to this term, we get our equivalent expression: p + 12y - 24. So, option A. p+ 12y - 24 is equivalent to 6(2y - 4) + p.
Learn more about Distributive Property here:https://brainly.com/question/37341329
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Joey bought 10 cupcakes and has four friends. He wants to have nothing left, but he wants everyone including him to have the same amount of cupcakes. How many cupcakes can each person get?
we use divsion, 10 divided by 5 is 2, everyone get 2 yumy cupcakes.